Equation 677 Database

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Magma eb0105cabf7a…

magma eb0105cabf7a
Size
705
Isomorphism class hash
eb0105cabf7a34cbb9cfa11720963585beb4c43986acafd8129a876aa433567e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 19:44:03
Display reorder
660,324,456,32,313,420,325,457,30,314,421,326,458,31,312,422,455,323,35,309,419,453,321,33,310,417,322,454,34,311,418,27,447,315,304,411,28,448,316,305,412,29,449,317,303,413,450,26,318,307,414,451,24,319,308,415,452,25,320,306,416,674,682,680,685,492,176,82,360,468,493,174,83,361,469,494,175,81,362,470,179,491,78,359,467,177,489,79,357,465,490,178,80,358,466,73,171,483,351,459,74,172,484,352,460,72,173,485,353,461,170,76,486,354,462,168,77,487,355,463,169,75,488,356,464,666,670,665,662,408,372,189,561,109,409,373,190,562,110,410,374,191,563,108,371,407,188,560,112,369,405,186,558,113,406,370,187,559,111,180,363,399,552,115,181,364,400,553,116,182,365,401,554,114,366,183,402,555,118,367,184,403,556,119,368,185,404,557,117,678,676,687,686,636,641,1,637,640,644,649,0,645,648,653,657,2,652,656,633,629,3,628,632,617,612,4,613,616,621,625,5,620,624,6,519,206,209,252,7,520,204,207,253,8,521,205,208,254,590,9,589,592,593,601,10,596,597,600,609,11,605,604,608,703,697,704,698,286,336,240,94,276,287,337,241,95,277,285,338,242,93,278,335,289,243,90,275,333,290,244,91,273,288,334,245,92,274,238,327,284,85,267,239,328,282,86,268,237,329,283,84,269,330,234,280,88,270,331,235,281,89,271,332,236,279,87,272,689,691,690,694,444,384,132,573,198,445,385,133,574,199,446,386,134,575,200,383,443,135,572,201,381,441,136,570,202,442,382,137,571,203,138,375,435,564,196,139,376,436,565,197,140,377,437,566,195,378,141,438,567,192,379,142,439,568,193,380,143,440,569,194,664,663,661,672,46,543,153,101,59,47,544,154,99,57,45,545,155,100,58,542,42,152,97,55,540,43,150,98,56,44,541,151,96,54,144,534,37,107,50,145,535,38,105,48,146,536,36,106,49,537,147,40,103,53,538,148,41,104,51,539,149,39,102,52,695,693,696,692,432,585,124,396,156,433,586,125,397,157,434,587,123,398,158,584,431,120,395,159,582,429,121,393,160,430,583,122,394,161,130,576,423,387,162,131,577,424,388,163,129,578,425,389,164,579,126,426,390,165,580,127,427,391,166,581,128,428,392,167,681,688,673,677,638,642,16,643,639,646,650,17,651,647,654,658,15,659,655,634,630,12,635,631,618,614,13,619,615,622,626,14,627,623,22,548,248,549,251,23,546,246,550,249,21,547,247,551,250,595,18,594,591,588,602,19,598,603,599,610,20,606,611,607,702,700,699,701,233,516,262,210,531,231,517,263,211,532,232,518,261,212,533,515,229,265,213,530,513,230,266,214,528,228,514,264,215,529,260,507,224,216,522,258,508,222,217,523,259,509,223,218,524,510,256,227,219,525,511,257,225,220,526,512,255,226,221,527,671,668,669,667,480,348,71,292,504,481,349,69,293,505,482,350,70,291,506,347,479,67,295,503,345,477,68,296,501,478,346,66,294,502,62,339,471,298,495,60,340,472,299,496,61,341,473,297,497,342,65,474,301,498,343,63,475,302,499,344,64,476,300,500,683,675,684,679 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#a687d51fdba056b88b615f4c33c4bd51079879725771af3a621b4a64ac93acf2, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 19:44:04 · history